CN112070200A

CN112070200A - Harmonic group optimization method and application thereof

Info

Publication number: CN112070200A
Application number: CN201910497327.7A
Authority: CN
Inventors: 郝志峰; 叶维彰; 刘翔宇; 王金海
Original assignee: Foshan University
Current assignee: Foshan University
Priority date: 2019-06-10
Filing date: 2019-06-10
Publication date: 2020-12-11
Anticipated expiration: 2039-06-10
Also published as: CN112070200B

Abstract

The present disclosure provides a harmonic group optimization method and application thereof, and provides a new continuous SSO integrated single variable update mechanism UM₁And a novel harmonic step size strategy HSS improves continuous simplified group optimization SSO, UM₁The HSS can balance the exploration and utilization capacity of the continuous SSO in the exploration of high-dimensional multivariable and multi-modal numerical value continuous reference functions; the update mechanism UM1 only needs to update one variable, and it is completely different from the variables in SSO in that all variables need not be updated; in said UM1, the HSS enhances the utilization capacity by reducing the step size based on the harmonic sequence; and numerical experiments were performed on 18 high-dimensional functions to confirm the efficiency of the method provided by the present disclosure; the method improves the exploration and utilization performance of the traditional ABC and SSO, obtains a relatively excellent balance point between the exploration and the utilization, has wide application range, and can greatly improve the classification and prediction precision of newly obtained big data by supporting an artificial neural network, a vector machine and the like.

Description

Harmonic group optimization method and application thereof

Technical Field

The disclosure relates to the technical field of soft computing application and big data processing, in particular to a harmonic group optimization method and application thereof.

Background

There are always a number of optimization problems in practical applications, such as green supply chain management, big data and network reliability problems. It is also common in real-world problems to apply small changes (e.g., integer variables, non-linear equations, and/or multiple objectives) to the optimization model. However, even if only integer variables are used, these real-life problems become very difficult to solve, and solving them using conventional methods within an acceptable time is more complicated and enormous. Therefore, the emphasis of recent various studies has shifted to producing high quality solutions using soft computing methods rather than precise solutions within an acceptable execution time, see references [1-26 ].

More and more new soft computing methods are emerging, such as artificial neural networks [2,37], Genetic Algorithms (GA) [3,4, 34], simulated annealing [5], tabu search [6], ant colony optimization [11], particle swarm optimization algorithms [7,8,34], differential evolution [9,10], algorithm estimated distributions [12], artificial bee colony Algorithms (ABC) [13-16], the simplified group optimization algorithm/simplified group algorithm (SSO)) [17-26], empire-oriented competition algorithm [35], reinforcement learning algorithm [36], Bayesian network [38], hurricane optimization algorithm [39], gravity search algorithm [40], human clustering [41], bat algorithm [42], random diffusion search [43] and the like are new soft computing methods, and the inspiration comes from the natural phenomenon of solving a larger problem in the scientific technology in recent years. Therefore, soft computing has attracted considerable attention and has been applied to a range of real-world problems, such as Swarm Intelligence (Swarm Intelligence) and evolutionary algorithms (EAs for short), see references [44] and [45], respectively.

In soft computing, local search based exploration is the finding of optimal behavior in a neighborhood of known solutions, increasing the chances of solution quality at the expense of capture of the locally best solution [2-26], and global search with emphasis on exploration refers to searching for optimal values in the unexplored solution space to avoid settling into partially optimal at run-time costs [2-26 ]. Exploration (exploration) and utilization (exploitation) are opposite, but complementary. It is worth noting that a balance of exploration and utilization is sought to ensure the implementation of any soft computing method.

The SSO (simplified group optimization algorithm/simplified group algorithm) introduced by Yeh, see reference: "Study on quick Path Networks with Dependent Components and Apply to RAP", Technical Report NSC97-2221-E-007-099-MY3, diagnostic subjects Research Project by National Science Council, Taiwan ] one of the newly proposed population-based (population-based) soft computing methods. SSO achieves very high efficiencies and efficiencies from previously known numerical experiments [17-26 ]. Furthermore, SSO can flexibly cope with various realistic problems, and is gradually applied to different optimization applications, such as supply chain management [20,21], redundancy allocation problems [18,19,27], data mining [20,21], and other optimization problems [32,33 ].

Total variable Update Mechanism (UM)_a) Is the basis for all variants of SSO, so all variables are updated in each solution. However, UM_aAlways exploring undiscovered solution spaces, even if best approaching the current solution [17-27,31,32]]It may also take additional time to reach the optimum.

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disclosure of Invention

The present disclosure provides a harmonic group optimization method and application thereof, in order to provide a new continuous SSO integrated single variable Update Mechanism (UM)₁) And a novel harmonic step size strategy (HSS) by introducing a univariate Update Mechanism (UM)₁) And a harmonic step size strategy (HSS) to improve successive simplified group optimization (SSO). The UM₁The HSS can balance the exploration and utilization capacity of the continuous SSO in the exploration of high-dimensional multivariable and multimode numerical value continuous reference functions; update mechanism UM₁Only one variable needs to be updated, and it is completely different from the variables in SSO and does not need to update all variables; in the UM₁The HSS enhances the utilized capacity by reducing the step size based on the harmonic sequence. And numerical experiments were performed on 18 high-dimensional functions to confirm the efficiency of the method provided by the present disclosure.

In order to achieve the above object, according to an aspect of the present disclosure, there is provided a harmonic group optimization method including the steps of:

step 1, constructing a harmonic step length strategy HSS;

step 2, establishing a univariate updating mechanism UM₁；

Step 3, passing UM₁Optimizing the SSO by the HSS to obtain the optimized SSO;

and 4, applying the optimized SSO to big data processing.

Further, in step 1, the method for constructing the harmonic step size strategy HSS includes: to improve exploration performance, a harmonic sequence-based HSS was constructed as shown below:

wherein N is_varIs the number of variables, U_kAnd L_kIs the upper and lower limits of the kth variable, i is the current generation, k is the index of the current variable, the sign

Is Floor function/Floor () function; referring to the sequence of 1,1/2,1/3,1/4 as harmonic sequence, the HSS can be expressed as follows based on the harmonic sequence:

step size Δ if each genetic cycle lasts 50 generations_i,kThe value of (a) is reduced from generation to generation of the generation period.

The gBest and some solutions are closer to the optimal state after long runs or generations, and the updates to these solutions need only be slightly changed to be closer to the optimal state without leaving the optimal region. Due to the reduction of the harmonic sequence, the step length is adjusted from a longer time generated in the early stage to a shorter time generated in the later stage of the HSS, thereby overcoming the defect of continuous SSO.

Further, in step 2, a univariate update mechanism UM is established₁The method comprises the following steps: in the main soft calculation, each solution is slightly updated, and in order to reduce the random number and gradually change the stability of the solution, the UM of each solution is made₁Only one randomly selected variable is updated, assuming i is the current generation number, x_j,kIs to solve X from the jth_jOf (a) a randomly selected variable of (b),

is obtained by modifying X_jX of_j,kThe obtained time solutionThe following equation can be obtained:

σ_k,1and σ_k,2Is respectively in [ -0.5,0.5 [ -0.5 [)]And [0, 1]]The uniform random variables generated in (1);

ρ_kis [0, 1]]The uniform random variables generated in (1); g_kRepresents P_gBestK (k) of^th) A variable;

L_kand U_kRespectively, the lower limit and the upper limit of the kth variable.

Note:

(1) UM proposed in the present disclosure₁Removing the first subscript and UM of each solution_aTo reduce run time, e.g. UM_aX in (1)_i,jAnd x_i,j,kSimplified to the proposed UM₁X in (1)_jAnd x_j,k。

(2) For simplicity and without loss of generality, the equations above are formulated to take into account the minimization problem.

(3)

If not after updating and substituting X^*Calculation of F (X)^*) It needs to be changed to its nearest boundary before.

For example, the following equation is prepared to be minimized:

gen is hereditaryThe algebra of (c);

wherein, the following properties are provided:

attribute 1: in the implementation of UM₁The number of expected comparisons and random values in each solution is then from 3 · N_varReduced to 3, N_varTo 1.

And (3) proving that: numerical pair UM for testing the feasibility of each updating variable_aAnd UM₁Are all one. However, for each solution, UM_aTesting each updated variable, while UM₁Only one variable is tested. Furthermore, for each solution, UM based on equation (4)_aThe expected number of comparisons was calculated as follows:

N_var·(3c_w+2c_g+c_r)≥N_var·(3c_w+3c_g+3c_r)＝3·N_var,

because c is_r<c_w<c_gAnd c_r+c_w+c_g1 and its and c_g、c_wAnd c_rComparing the probabilities in the first, second and third terms of equation (4) 1,2 and 3 times, we can get:

(c_g+2c_w+3c_r)≤(3c_g+3c_w+3c_r)＝3。

further, in step 3, the UM is passed₁And the method for optimizing the SSO by the HSS comprises the following steps: the improved continuous SSO process proposed by the present disclosure is described as follows:

and step 0, making i-j-gBest-1.

Step 1, by X_jAnd calculating F (X)_j)；

Step 2, if F (X)_gBest)<F(X_j) Let gBest be j;

step 3, if j<N_solLet j equal to j +1 and go to step 1;

step 4, let n^*＝1，N^*50, and order

Wherein k is＝1,2,…,N_var；

Step 5, making i ═ i +1 and j ═ 1;

step 6, from X_jIn which a variable, e.g. x, is randomly selected_j,k；

Step 7, let

Step 8, order

Step 9, if F (X)^*)<F(X_j) Then let X_j＝X^*Turning to the step 10, otherwise, turning to the step 11;

step 10, if F (X)_j)<F(X_gBest) Let gBest be j;

if the current running time is equal to or greater than T, the process ends, step 11, and X_gBestIs suitable for F (X)_gBest) The final solution of (2);

step 12, if j<N_solLet j equal j +1 and go to step 6;

step 13, if i<N^*Go to step 5;

step 14. mixing n^*Increase by 1, N^*Increase by 50, and order

Wherein k is 1,2, …, N_varAnd the process goes to step 5,

wherein,

for the optimum k variable, x_i,j,kFor the current value of the kth variable in the jth solution,<<Δ_k，Δ_kis the step size, and Δ_kFor example, if 100. delta. is equal to_kIs the best case, x_i,j,kWill require 100 generations to converge to

Further, in step 4, the application method of the optimized SSO in the big data processing through the artificial neural network is as follows:

step A1, collecting big data conforming to the big data type;

step A2, preprocessing and cleaning the acquired big data, and extracting a data set obtained after the big data is cleaned;

step A3, performing dimension reduction on the cleaned data set;

step A4, dividing the data set after dimensionality reduction into a data set divided into a training set and a test set;

step A5, determining a three-layer perceptron neural network with an artificial neural network structure of 6-5-1, wherein the neural network needs to optimally design 41 parameters, and the value range of the optimal design parameters of the neural network is [ -1,1 ];

step A6, determining the input variable of the artificial neural network as big data conforming to big data type, and the output variable of the artificial neural network as big data output;

step A7, determining input variables and output variables of the artificial neural network;

step A8, mixing X in each optimized SSO_jThe variable in the method is decoded into parameters to be optimized of the artificial neural network, the error of the neural network after training a training set and/or a testing set is calculated, and the calculated error is used as the fitness F (X)_j) Inputting the result into the optimized SSO, and obtaining the suitable F (X) obtained from the operation result of the optimized SSO (the operation result of step 0 to step 14)_gBest) Of (2) a final solution X_gBestDecoding parameters of the artificial neural network, and taking the obtained artificial neural network as a classification model;

step A9, classifying the newly collected big data which accords with the big data type through a classification model;

the big data conforming to the big data type comprises but is not limited to any big data conforming to the data type of traditional enterprise data, machine and sensor data and social data; traditional enterprise data includes customer data from CRM systems, traditional ERP data, inventory data, and accounting data, among others. Machine and sensor data includes call logs, smart meters, industrial equipment sensors, equipment logs, transaction data, and the like. Social data includes user behavior records, feedback data, and the like. Social media platforms such as Twitter, Facebook.

Wherein, the big data output includes but is not limited to data category confidence and predicted value in any period of time in the future.

The application of the optimized SSO can greatly improve the classification precision or the prediction capability of the newly obtained big data of the artificial neural network.

Further, the method for applying the optimized SSO to big data processing through a support vector machine is as follows:

step B1, collecting big data conforming to the big data type;

step B2, preprocessing and cleaning the acquired big data and extracting features to obtain the feature vector of the big data;

step B3, using the feature vector of the big data as a training data set;

step B4, j uniform random variables are randomly generated, and the random variable set is X_j，X_jEach randomly selected variable in the vector machine stores a penalty factor C and a radial basis kernel parameter g of the support vector machine;

step B5, calculating X_jFitness F (X)_j) Inputting the result into the optimized SSO, and obtaining the suitable F (X) from the operation result of the optimized SSO (the operation results of step 0 to step 14)_gBest) Of (2) a final solution X_gBestDecoding the parameters into parameters of a support vector machine, and taking the obtained support vector machine as a classification model;

step B6, classifying the newly collected big data which accords with the big data type through a classification model;

the big data conforming to the big data type comprises but is not limited to any big data conforming to the data type of traditional enterprise data, machine and sensor data and social data; traditional enterprise data includes customer data from CRM systems, traditional ERP data, inventory data, and accounting data, among others. Machine and sensor data includes call logs, smart meters, industrial equipment sensors, equipment logs, transaction data, and the like. Social data includes user behavior records, feedback data, and the like.

Big data output includes, but is not limited to, data classification result, category confidence, among others.

The application of the optimized SSO can greatly improve the classification precision of the newly obtained big data by the support vector machine.

The beneficial effect of this disclosure does: the invention provides a harmonic wave group optimization method and application thereof, which improve the exploration and utilization performance of the traditional ABC and SSO, obtain a balance point with better quality between the exploration (exploration) and the utilization (exploration), have wide application range, can be applied to artificial neural networks, Genetic Algorithms (GA), simulated annealing, taboo search, ant colony optimization, particle swarm optimization, differential evolution, algorithm estimation distribution, artificial bee colony Algorithm (ABC), imperial competition algorithm, reinforcement learning algorithm, Bayesian networks, hurricane optimization algorithm, gravitation search algorithm, human colony, bat algorithm, random diffusion search and other methods for seeking optimized solutions, can be directly applied to the fields of big data processing, image processing, audio and video recognition and the like after parameter and other variable optimization adjustment is carried out by the disclosed method, and can greatly improve the fields of supporting artificial neural networks, image processing, audio and video recognition, The classification and prediction precision of newly obtained big data by a vector machine and the like; the accuracy and speed of image processing and audio and video recognition are improved.

Drawings

The foregoing and other features of the present disclosure will become more apparent from the detailed description of the embodiments shown in conjunction with the drawings in which like reference characters designate the same or similar elements throughout the several views, and it is apparent that the drawings in the following description are merely exemplary of the present disclosure from which other drawings may be derived without inventive effort to those skilled in the art, and in which:

FIG. 1 is a bar graph of the average success rate of SSO1 at different values of Δ and T in experiment 1;

FIG. 2 is a bar graph of SSO1 mean success rate and problems in experiment 1 for different Δ values and problems;

FIG. 3 is F obtained from ABC, GA, PSO, SSO1 and SSOa in experiment 2_minA value bar graph;

FIG. 4 is a histogram of AIO (ABC, SSO1), AIO (SSOa, SSO1), and AIO (ABC, SSOa);

FIG. 5 is a bar graph of success rates at different T values for experiment 2;

FIG. 6 is F for ABC, SSO1, and SSOa in experiment 2_minA value bar graph;

fig. 7 is a box plot of mean fitness values for ABC, SSO1 and SSOa at T1.25 in experiment 2;

fig. 8 is a box plot of mean fitness values for ABC, SSO1 and SSOa for experiment 2 at T ═ 1.50 (a);

fig. 9 is a box plot of mean fitness values for ABC, SSO1 and SSOa for experiment 2 at T ═ 1.50 (b);

fig. 10 is a box plot of the mean fitness values for ABC, SSO1 and SSOa for experiment 2 at T ═ 1.75;

fig. 11 is a box plot of the mean fitness values for ABC, SSO1 and SSOa at T2.00 in experiment 2;

fig. 12 is a box plot of the mean fitness values for ABC, SSO1 and SSOa at T2.25 for experiment 2;

fig. 13 is a box plot of the mean fitness values for ABC, SSO1 and SSOa for experiment 2 at T2.50;

fig. 14 is a box plot of the mean fitness values for ABC, SSO1 and SSOa for experiment 2 at T2.75;

fig. 15 is a box plot of the mean fitness values for ABC, SSO1 and SSOa for experiment 2 at T3.00;

fig. 16 is a box plot of the mean fitness values for ABC, SSO1 and SSOa for experiment 2 at T3.50;

fig. 17 is a box plot of the mean fitness values for ABC, SSO1 and SSOa for experiment 2 at T-3.75.

Detailed Description

The conception, specific structure and technical effects of the present disclosure will be clearly and completely described below in conjunction with the embodiments and the accompanying drawings to fully understand the objects, aspects and effects of the present disclosure. It should be noted that the embodiments and features of the embodiments in the present application may be combined with each other without conflict.

Simplified group optimization (SSO) overview:

methods for continuous SSO treatment of variables are described in references [23-25 ].

On the basis of the conventional SSO, a new continuous SSO is proposed. Hereinafter, a conventional SSO is briefly introduced before a new SSO proposed by the present disclosure is proposed.

Conventional (discrete) SSO

Conventional (discrete) SSO very effectively solves the discrete (optimization) problem (discrete variables only) [17-21,32] or the floating point limited continuous problem [22], e.g., the number of functions per value is limited in the data mining problem.

The basic idea of all types of SSO is that each variable, such as x_i+1,j,kBoth need to be updated according to the following equation:

where x is a randomly generated feasible value. For details, see references [17-27,31,32 ].

c_g、c_p、c_wAre parameters.

Based on the step function shown in equation (1) and the generated random number ρ_kDiscrete SSO updates each variable by verifying the first to last term in the step function until an interval is found that contains the generated random number.

Discrete SSO updates each variable only to a low probability value, c, that never occurred before_r. Thus, in most cases, discrete SSO can only update variables to a limited number of values, namely gBest, pBest and themselves, and these values are found only in all previous values. Furthermore, the utility modelAnd (5) carrying out a new process. The above advantages make discrete SSO very effective in solving the discrete problem, see references [17-22,32 ]]。

Continuous type SSO:

for a general continuous optimization problem, every variable of the final solution in the continuous optimization problem may never be found in all previous update processes. Therefore, there is a need to modify discrete SSOs for continuous problems without losing the simplicity and convenience of discrete SSOs [23-27,32 ]. Note that the advantages of continuous SSO are just the disadvantages of discrete SSO, and vice versa.

The basic flow of SSO variables has never changed, but is based on the step function of updating variables listed in equation (1), see references [17-27,31,32 ]. To date, the main trend in developing continuous SSO has been to add a step function to certain terms in equation (1) (see references [23-25]), or to combine SSO with other soft computing methods [26,27,31], such as differential evolution (see references [26,31]) and PSO (see references [ c.l. huang, "a particulate-based simplified timing optimization for reproducibility recovery schemes", Reliability Engineering & System Safety volume, 142, pp.221-230,2015 ]).

The all-variable update mechanism in SSO (e.g., equation (1)) can escape local optimization and explore unreachable/unrealized spaces. Therefore, the goal of continuous SSO is to explore a better approach in exploration, the main step is to add a random step size in some items of the update mechanism, which is obtained by multiplying some random number by the step size. As with the method identified by the present disclosure, we will explore better step sizes for the main purpose of the present disclosure.

Yeh first proposes a continuous SSO by adding step length to the update mechanism for predicting Time Series questions (W.C. Yeh, "A New Parameter-Free Simplified switch Optimization for architectural New Network routing and applications in Prediction of Time-Series", IEEE Transactions on Neural Networks and Learning Systems, vol, pp.661-665,2013), as shown below

Wherein sigma_kIs in [ -1,1 [)]Uniform random numbers generated within the range, step size Δ_jIs the reciprocal of the number of genetic generations for which the adaptability of the ith solution has not improved.

Note that equation (2) is also the first adaptive parameter concept, which uses the parameter c_g(represented by c in the formula (2))_g,i,j) And c_w(represented by c in the formula (2))_w,i,j) As a variable, each solution thus has its own c in SSO_gAnd c_w. See the references [ W.C. Yeh, "A New Parameter-Free matched Optimization for architectural Neural Network routing and its applications in Prediction of Time-Series", IEEE Transactions on Neural Networks and Learning Systems, vol.24, pp.661-665,2013 ], which is different from conventional SSO in that all parameters of the SSO are fixed from start to finish.

To determine the step size Δ_jStill too large a value of [23,24 ]]Yeh proposes a new UM (referred to herein as UM) even for larger generations in equation (2)_a) Updating all continuous variable intervals-1, 1 by shortening]To [ -0.5,0.5 [)]Will be a_jInstead, it is changed into

And further multiplied by a random number in equation (2) (see references [ K.kang, C.Bae, H.W.F. Yeung, and Y.Y.Chung ] "A Hybrid graphical overview Search with switch understanding and Deep conditional feed for Object Tracking Optimization", Applied Soft Computing, https:// doi.org/10.1016/j.asoc.2018.02.037, 2018) ] as follows.

Wherein,

c_g、c_ris a parameter, N_varIs the number of variables. Sigma_1,kAnd σ_2,kIs in the range of [ -0.5,0.5 [)]Two uniform random variables generated in (1);

ρ_kis at [0, 1]]The uniform random variables generated in (1); u shape_kAnd L_kAre the upper and lower limits of the kth variable.

In equation (3), the solution can only be updated to a better value; otherwise, UM_aThe original solution (4) is preserved before updating as UM_aThe most important part of this, the concept behind it is that each variable is updated to its own neighborhood, the gBest neighborhood, and the interval between itself and the gBest (if ρ)_kAt and c_r(first term in formula (4)), c_g(second term in formula (4)) and c_w＝1-c_r-c_g(third term in the formula (4)).

Note:

1. modified reference of formula (4) [25]Error in (2), which is a loss of ρ_2,var。

2. In equation (4), if the updated variable is not feasible, it is set as the nearest boundary.

The disadvantages of current continuous SSO are:

in the prior continuous SSO proposed in references 23-25, the step size is fixed and every variable requires the step size of all genetic algebras.

Starting from equation (2), the step size ρ is random_k·Δ_jHas a minimum value of 1/N_genOnly at

ρ

_k1 and 1/delta_j＝N_genI.e. the jth solution is not improved from start to finish. For example, if it is N_gen1000 is then ρ_k·Δ_j-0.001. For some special problems, the above values are still too large,and therefore too far from the optimum.

In equations (4) and (5), if the step size Δ is close to the end of the current generation number_kToo long, the update mechanism is not available, causing it to converge to an optimal value. On the contrary, if the step size Δ_kToo short and the solution is not sufficiently momentum, it takes a long time to reach around the optimum, especially at an early stage.

For example, let the current value of the kth variable in the jth solution be x_i,j,kThe k-th variable is

If so<<Δ_kOr even delta_kNeeds to be calculated at [ -0.5,0.5 [)]Two different random numbers are generated in, then there is little likelihood that the next updated solution will be close to optimal. However, if 100. delta. is equal to_kIs the best case, x_i,j,kWill require 100 generations to converge to

Therefore, it is more reasonable to have an adaptive step size instead of a fixed step size in the exploration. Thus, the present disclosure proposes a new HSS-based continuous SSO update mechanism.

UM proposed by the present disclosure₁And HSS:

to improve exploration performance, the harmonic sequence based HSS proposed by the present disclosure is presented in equation (6) as follows:

wherein N is_varIs the number of variables, U_kAnd L_kIs the upper and lower limits of the kth variable, i is the current algebra, k is the index of the current variable, the sign

Is the Floor function/Floor () function.

If the sequence of 1,1/2,1/3,1/4 is referred to as a harmonic sequence, the harmonic-based sequence HSS proposed by the present disclosure can be represented as follows:

if each genetic cycle lasts 50 generations. Step size Δ_i,kThe value of (a) is reduced from generation to generation of the generation period. Shown in table 1 as HSS-based (if U)_k-L _k10 and N_var100) step size.

Table 120 steps

Period i	1	2	3	4	5	6	7	8	9	10
											Δ_i,k	0.08000	0.04000	0.02667	0.02000	0.01600	0.01333	0.01143	0.01000	0.00889	0.00800
Period i	11	12	13	14	15	16	17	18	19	20
											Δ_i,k	0.00727	0.00667	0.00615	0.00571	0.00533	0.00500	0.00471	0.00444	0.00421	0.00400

The gBest and some solutions are closer to the optimal state after long runs or generations. The update of these solutions need only be slightly changed to get closer to the optimal state without leaving the optimal area. Due to the reduction of the harmonic sequence, the step length is adjusted from a longer time generated in the early stage to a shorter time generated in the later stage of the HSS, thereby overcoming the defect of continuous SSO.

Single variable UM (UM)₁)

In the main soft calculation, each solution is slightly updated. For example, the UM of a PSO is a vector-based UM that is the two equations listed below, specifically (see references [7,8,27 ]):

V_i+1,j＝wV_i,j+c₁·σ₁·(G-X_i,j)+c₂·σ₂·(P_i-X_i,j) (8)

X_i+1,j＝X_i,j+V_i+1,j (9)

wherein, V_i,jAnd X_i,jThe velocity and position of the jth particle in the ith generation respectively;

w、c₁、c₂is a constant; sigma₁And σ₂Is in the interval [0, 1]]Two uniform random variables are internally generated; p_iIs pBest solving i;

G＝P_gBestis gBest. Note: p in SSO_gBestEqual to G in formula (8).

In ABC (see references [13-16]), a variable is randomly selected for each solution to be updated. The update operator in the conventional Genetic Algorithm (GA) (see references [3,4]) can change half of the variables by one cut-point crossing, and can also update two variables by one cut-point mutation. However, in SSO, all variables must be updated.

In order to reduce random numbers and gradually change the stability of the solutions, UM for each solution₁Only one randomly selected variable is updated. Let i be the current number of generations, x_j,kIs to solve X from the jth_jOf (a) a randomly selected variable of (b),

is obtained by modifying X_jX of_j,kThe resulting time solution. The following equation can be obtained:

ρ_kis [0, 1]]The uniform random variables generated in (1);

Note:

(3)

For example, the following equation is prepared to be minimized:

table 2 shows the proposed UM basis₁Different rho of₁Updating of the value X₇。

TABLE 2 UM₁Examples of (2)

Marking^！Is from 1.216>U₁1.0 for onset

Replacement of

Marking^！！Is from F (X)₇)＝F(-0.41467,-0.3)＝0.008395<F(X_gBest) F (-0.5, -0.9) ═ 0.0596 begins with gBest ═ 7 replacing gBest ═ 3.

Therefore, the following lemma is true.

N_var·(3c_w+2c_g+c_r)≥N_var·(3c_w+3c_g+3c_r)＝3·N_var, (15)

because c is_r<c_w<c_gAnd c_r+c_w+c_g1 and its and c_g、c_wAnd c_rIn the first of formula (4)The probabilities in the second and third terms are compared 1,2 and 3 times to obtain:

(c_g+2c_w+3c_r)≤(3c_g+3c_w+3c_r)＝3， (16)

if UM is implemented based on equation (11)₁Then σ is required for each variable in equation (4)_var,1，σ_var,2And ρ_varBut only for each variable in equation (11).

The improved continuous SSO process proposed by the present disclosure is described as follows:

and step 0, making i-j-gBest-1.

Step 1, create an arbitrary X_jAnd calculating F (X)_j)；

Step 2, if F (X)_gBest)<F(X_j) Let gBest be j;

step 3, if j<N_solLet j equal to j +1 and go to step 1;

step 4, let n^*＝1，N^*50, and order

Wherein k is 1,2, …, N_var；

Step 5, making i ═ i +1 and j ═ 1;

step 6, from X_jIn which a variable, e.g. x, is randomly selected_j,k；

Step 7, let

Step 8, order

step 10, if F (X)_j)<F(X_gBest) Let gBest be j;

step (ii) of11, if the current running time is equal to or greater than T, the flow ends, and X_gBestIs suitable for F (X)_gBest) The final solution of (2);

step 12, if j<N_solLet j equal j +1 and go to step 6;

step 13, if i<N^*Go to step 5;

step 14. mixing n^*Increase by 1, N^*Increase by 50, and order

Wherein k is 1,2, …, N_varAnd go to step 5.

Wherein,

for the optimum k variable, x_i,j,kFor the current value of the kth variable in the jth solution,<<Δ_k， Δ_kis the step size, and Δ_kFor example, if 100. delta. is equal to_kIs the best case, x_i,j,kWill require 100 generations to converge to

Examples evaluation of properties:

in this example, two experiments, experiment 1 and experiment 2, were performed based on 18 continuous numerical functions of 50 variables extending from the baseline problem, see references [13-16,26,25], as shown in the experimental data of Table A. Data type flags in the experimental data of table a include C: characteristic data, U: unimodal data, M: multimodal data, S: separable data, N: data is not separable.

TABLE A Experimental data

Experiment design:

for ease of identification, the SSO of UMa proposed in reference [25] (k.kang, c.bae, h.w.f.yuung, and y.y.chung, "a Hybrid qualitative Search Algorithm with switch intelligent and Deep conditional feed for Object Tracking Optimization", Applied Soft Computing, https:// doi.org/10.1016/j.asoc.2018.02.037, 2018) is referred to as SSOa, and the SSO implemented by HSS and UM1 in this example is referred to as SSO1 in this example.

In experiment 1, only the role of the HSS and the different associated step size strategies were tested to determine the optimal value of the step size in the proposed HSS. The step size with the best results in experiment 1 was used in SSO1 of experiment 2.

In experiment 2, the emphasis was shifted to comparing the performance of SSO1 with the other four algorithms: ABC [13-16], SSOa [25], GA [3,4] and PSO [7,8 ]; GA and PSO are two most advanced algorithms in evolutionary computation and population intelligence; ABC [13-16] and SSOa [25] are the most common algorithms of the 50 well-known benchmark problems, with variables less than or equal to 30, if the stopping criteria are fitness function evaluation number and run time, respectively.

Each algorithm tested in all experiments was written in the C programming language. Wherein, ABC code is adapted from http:// mf.

SSOa, GA and PSO are all from http:// integration and chromatography. Each test was applied to Intel Core i7-5960X CPU 3.00GHz, 16GB RAM and 64 bit Win10, run time units CPU seconds.

In all tests, all parameters applied in SSO1, SSOa and ABC during the experiment were directly from the reference [25]]For a more accurate comparison: c. C_r＝0.45，c_g＝0.40，c_w＝0.15。

For ABC, references [13-16] are used for all parameters. The bee colony size was 50, the number of food sources was 25, and if no improvement was observed after 50 · 25 updates to 750 times, the solution was regenerated.

For GA, one-point crossover, two-point mutation and elite selection were achieved with crossover rate 0.7 and mutation rate 0.3, respectively, see references [3,4 ].

For PSO, c in formula (4)_w0.9 and c₁＝c₂2.0; setting the speed function to be in the range of 2 or-2 if the value of the speed function is greater than 2 or less than-2 [7,8]]。

ABC may calculate fitness values more than once in each generation, see references [13-16], and therefore, using the number of heritage as a stopping criterion is incorrect and unfair.

In addition, the second UM in ABC, the "onlooker", takes extra time to update the solution.

Thus, for a fair comparison, the time limit (denoted by t) of 1.25,1.50 … … to 3.75 computer seconds for each algorithm in experiment 2 was used as a stopping criterion to observe the trend and change of each algorithm.

Note: each run is independent for all three algorithms. For example, in the case of t 1.50, each run SSO1 must be restarted from 0 seconds, rather than simply extending from t 1.25 times 0.25 seconds to any run

For each benchmark function, the average run time is the time to obtain 50 gBest. In all tables, each subscript represents the ranking of the values. Furthermore, N_run55 and N_sol＝100。

In practical applications, algorithms are implemented and executed numerous times to find the best result. Only the solution with the best results is retained and used. Therefore, most of the related published papers are only illustrative by simply reporting and comparing the best results obtained from the algorithms, see references [13-16,25,27 ]]. Therefore, the disclosure also focuses on the best results F in experiment 2_min。

Experiment 1 finding the optimal step size Δ:

experimental results of experiment 1, including F_avg、F_min、F_max、F_stdSuccess rate (percentage of cases that successfully solved the problem), and the step length based Δ of experiment 1 ═ 1.0The number of fitness function calculations of (1.25) and (1.50) of 55 runs over 3.70 seconds as shown in table 3 and fig. 1 and 2, fig. 1 is the average success rate of SSO1 at different values of Δ and T in experiment 1, and fig. 2 is the average success rate of SSO1 at different values of Δ and problems in experiment 1.

Although all correlation values in table 3 tend to decrease as T increases, some fluctuation is found, for example, F at T2.00_avg0.04467947084586 improves to 0.03980129242576 at T2.25 and then decreases to 0.06607165055859 at T2.50 at Δ 1.25 due to the randomness of the soft calculations and independence of each run.

From Table 3, it can be seen that Δ ≧ 1.25 has the optimum F for T ≧ 2.00 (except T ≧ 3.50)_minOptimum F for T ═ 1.50, 2.00,2.25 and 2.75_avg、F_maxAnd F_std(ii) a For T1.75, 3.25 and 3.50, Δ 1.00 has the best F_avg、F_min、F_maxAnd F_std(except that F when T is 3.25_min) (ii) a For F_avg，F_maxAnd F_stdΔ ═ 1.75 is the optimum of the minimum and maximum T, i.e., T ═ 1.25 and T ═ 3.75.

Table 3 results obtained from different delta values in experiment 1

Fig. 1 and 2 show the average success rates for different values of t and baseline problems, respectively. The success rate is defined as the percentage of the final gBest that is equal to the best solution. For example, a success rate of 62.020% means 100 · 55 · 18 ═ 99,000 for Δ ═ 1.25 and t ═ 1.25, and finally 62.020% of gBest equals the relevant optimization, where N is equal to N_sol＝100，N_runWhere 18 is the number of benchmark questions.

From the above it can be observed that Δ 1.25 always has the best success rate on average for different T values and reference problems in fig. 1 and 2. Note that the difference between Δ ═ 1.25 and Δ ═ 1.00 and between Δ ═ 1.25 and Δ ═ 1.50 is up to 27%, i.e., the probability that Δ ═ 1.25 obtains the optimum value is 27% higher than that of Δ ═ 1.00 and Δ ═ 1.50. SSO1 at Δ ═ 1.25 can solve 14 of the 18 baseline problems, which is also the best of the three settings of Δ.

As can be seen from table 3 and fig. 1 and 2, Δ ═ 1.25 is superior to 1.00 and 1.50 in the quality of the solution. Therefore, Δ is used in the proposed HSS and experiment 2 as 1.25 without further optimization of Δ.

Experiment 2: comparison between ABC, GA, PSO, SSO1 and SSOa:

f obtained from five test algorithms (i.e., ABC, GA, PSO, SSO1, and SSOa) from 55 runs within 3.70 seconds of T ═ 1.25,1.50_minThe average values of (A) are shown in FIG. 3, and FIG. 3 is F obtained from ABC, GA, PSO, SSO1 and SSOa in experiment 2_minThe value is obtained. The results obtained from ABC, SSO1 and SSOa are shown in FIG. 6 together with 11 box plots in the box plots for the average fitness values of ABC, SSO1 and SSOa for experiments 2 with T values of 1.25,1.50 (a), 1.50(b), 1.75, 2.00,2.25, 2.50, 2.75, 3.00, 3.50, 3.75, respectively, as shown in FIGS. 7,8, 9,10, 11, 12, 13, 14, 15, 16, 17 for experiment 2, and for ABC, SSO1 and SSOa, respectively, FIG. 6 is the F for ABC, SSO1 and SSOa_minA bar graph of values, graphically depicting the overall results. Note: these 11 box plots also show the best results. Furthermore, to obtain more detail about the basic part of the result (the average from the best quartile to the third quartile), the third quartile to average worst fit result is truncated.

Average F Using SSO1 with ABC and SSOa_minThe improvement rates (AIO), such as AIO (ABC, SSO1) and AIO (SSOa, SSO1), are shown in fig. 4, which is a histogram of AIO (ABC, SSO1), AIO (SSOa, SSO1), and AIO (ABC, SSOa).

Wherein,

wherein, both alpha and beta represent a test algorithm;

the associated success rates are summarized in fig. 5, and fig. 5 is a bar graph of the success rates at different T values in experiment 2. The number of fitness function calculations is shown in table 4.

In addition, some fluctuations were observed in some results of experiment 2. These fluctuations are caused by the random nature of the soft computing and the fact that each run is independent.

Table 4 number of fitness function calculations in experiment 2

Comprehensive analysis of the quality of solutions

FIGS. 3, 6, and 7 emphasize the effectiveness (i.e., quality of solution) of ABC, SSO1, and SSOA. As can be seen from fig. 3, both the genetic algorithm and the particle swarm algorithm performed much worse than the other three algorithms. This observation was made in other studies [13-16 ]. Furthermore, as the running time increases, the weaknesses of genetic algorithms and particle swarm algorithms become more pronounced. Thus, the remainder of the disclosure focuses only on ABC, SSO1, and SSOA.

As shown in fig. 7,8, 9,10, 11, 12, 13, 14, 15, 16, and 17, which are box charts of average fitness values of ABC, SSO1, and SSOa at values of T in experiment 2 of 1.25,1.50, 1.75, 2.00,2.25, 2.50, 2.75, 3.00, 3.50, and 3.75, respectively, the results are closer to the best solution as the operation time increases. As can be seen from FIG. 6, FIG. 6 shows F of ABC, SSO1 and SSOa in experiment 2_minThe value bar graph, ABC, is better than SSO1 and SSOa for smaller run times, e.g., T1.25 and T1.50. However, due to modern advanced computer technology, the small "run-time" dependencies are not important. On the contrary, in the case of T ≧ TSSO1 outperformed ABC after 2.75 seconds, while SSOa outperformed average F for all Ts_min. For T3.75, the gap between SSO1 and ABC reaches almost 0.01, and the gap between SSO1 and SSOa is almost 0.005. Furthermore, ABC for F when T increases_avgThe SSO1 of (a) did not improve to the same extent. The above results provide evidence that ABC is easily trapped in a local optimum of a large T.

As shown in figures 7,8, 9,10, 11, 12, 13, 14, 15, 16 and 17,

ABC produces better F_maxAnd F_stdThe value is obtained. In contrast, SSOa produces F_maxAnd F_stdThe worst value of (c). The reason for this result is that UMa used in SSOa must update all variables, whereas only one variable was selected in ABC and UM1 was used in SSO1 for each solution of each generation. Another reason ABC is always more powerful than SSO1 and SSOa is that ABC easily traps local traps and lacks the ability to escape local optima.

In summary, the SSO1 method proposed by the present disclosure has significant advantages over other methods.

Average F_minImprovement rate (AIO)

To measure the amount of improvement in average Fmin obtained from ABC, SSO1 and SSOa, the average Fmin improvement rate (AIO) is given in fig. 4, where AIO is defined as follows from ABC to SSO1, namely AIO (ABC, SSO 1):

measurement of F between ABC and SSO1 by AIO (ABC, SSO1)_minTo improve one F in SSO1_minThe higher the AIO (ABC, SSO1), the more effective the SSO1, and vice versa. For example, for T3.75 in fig. 4, AIO (ABC, SSO1) ═ 55.673% indicates the average F of SSO1_minOne unit improvement of (A) will result in an average F of ABC and SSO1_minThe difference between increases 0.55673. Likewise, AIO (SSOa, SSO1) and AIO (ABC, SSOa) are available.

As can be seen from fig. 4, the value of AIO (ABC, SSO1) increased from-21.227% (worst) of T1.25 to 55.673% (best) of T3.75; AIO (ABC, SSOa) decreases from 48.396% (best) at T ═ 1.25 to 4.936% (worst) at T ═ 3.25, and then increases to 29.960% at T ═ 3.75. Thus, the following conclusions can be drawn:

SSO1 always performs much faster than ABC, i.e., ABC and F increase as T increases_avgThe SSO1 was not improved to the same extent compared to.

2. Average F of SSOa from T ═ 1.25 to T ═ 3.25_minThe improvement tends to be similar to the average improvement of SSO 1. However, after T3.25, the performance of SSO1 improved more than SSOa.

The quality and robustness of the solution of SSOa exceeds ABC.

The reason for these conclusions is that the third UM "scout" is not very effective in evading local optimality, because ABC is designed to randomly regenerate the current solution if it does not improve in a predetermined number of iterations. In addition, UM used in SSOa_aAll variables need to be updated, which makes it more powerful in a global search, but gradually and slowly improves the quality of its solution.

Success rate:

fig. 5 shows that the success rate of the correlation value is at most 0.0001 greater than the exact solution, which is desirable because the correlation value should be as close to the exact value as possible. Fig. 5 shows similar observations as shown in fig. 7. For T<2.75 patients, ABC has a better success rate, but for F_minSSO1 always has a better success rate.

The effect is as follows:

table 4 shows mainly the number of computations for the fitness function to compare the efficiency between ABC, SSO1 and SSOA.

N_ABCIs the total number of fitness functions, n_ABCIs the calculation to obtain the best final solution from ABC. N is a radical of_SSO1And n_SSO1Pairs of and N_SSOaAnd n_SSOaThe constituent pairs are related to N in the sense that they are related to each other_ABCAnd n_ABCIn parallel, since both components of each pair use the same algorithmDerived (N)_SSO1And n_SSO1From algorithms SSO1 and N_SSOaAnd n_SSOaFrom the algorithm SSOa. )

In Table 4, the ratio n_ABC/N_ABCLess than 42%, i.e., after 42% of the number of calculations of the fitness function of ABC, the final best solution never changes. Furthermore, as the operating time increases, the ratio n_ABC/N_ABCAnd decreases. These two observations further demonstrate that ABC is well suited for local search, but global search capability is weak. Ratio N_SSO1/N_ABCSum ratio N_SSOa/N_ABCAre both greater than 918, and nSSO1/nABC and n_SSOa/n_ABCAre each at least 2,100. Therefore, UM₁And UM_aAre all at least 918 times faster than the UM implemented in ABC, i.e., UM₁And UM_aMore efficient than ABC. N in Table 4_SSOa/N_SSOaAnd n_SSO1/N_SSO1The proportions of (a) are at least 95.5% and 95.47%, respectively. Thus, in contrast to ABC, SSO1 and SSOa continue to improve their solutions almost at the end of their respective runs, i.e., SSO1 and SSOa are very strong global search algorithms.

Based on these observations, SSO1 achieves a better balance between exploration and utilization than ABC and SSOa.

And (4) conclusion:

in the embodiments of the present disclosure, UM₁One variable in each solution is updated to improve the exploration capability of SSO and a new HSS is introduced to replace the fixed step size to improve the utilization capability of SSO.

Through extensive experimental studies of 18 high-dimensional functions, the resulting Δ ═ 1.25 HSS achieved better performance than Δ ═ 1.00 and Δ ═ 1.50. Furthermore, the proposed UM1 uses the proposed HSS for Δ ═ 1.25, achieving a better compromise between exploration and utilization than ABC, GA, PSO and SSOa.

Note: ABC always has a smaller deviation, which makes it more robust than SSO1 and SSOa because it is less prone to fall into local optima than SSO1 and SSOa.

However, the proposed algorithm of the present disclosure still has some limitations, however, still has some limitations for the proposed algorithm, even including ABC, GA, PSO, SSOa and all current soft calculations: a) among some of the problems with the analysis benchmark, the configuration considered globally optimal does not have the highest performance; b) the proposed heuristic requires knowledge of the limits (upper and lower) of the optimal values. Therefore, the proposed algorithm has to be improved to overcome the two main obstacles described above.

Although the results of the algorithm proposed by the present disclosure are superior to ABC and SSOa in both solution quality and efficiency. The algorithm proposed by the present disclosure may be sensitive to constant parameters. Therefore, considering the evolution process of SSO, its sensitivity aspect will be explored in future work to adjust the step size.

Abbreviations/terms

Δ represents a step size (step length);

ρ_kis represented by [0, 1]]A uniform random number created from the kth variable (kth);

ABC represents an artificial bee colony algorithm;

AOI denotes F_minAverage F_minThe improvement rate;

F(X_i,j) Represents X_i,jA fitness function of;

gBest represents the historically best solution;

pBest represents its own historically best solution;

F_avgrepresents the average fitness of the 50 best gBest;

F_maxrepresents the worst fitness of the 50 best gBest;

F_minrepresents the best fitness of the 50 best gBest;

F_stdthe fitness standard deviation of the 50 best gBest is shown;

GA represents a genetic algorithm;

g_krepresents P_gBestK (k) of^th) A variable;

N_●represents the mean fitness metric evaluation number of the algorithm ●;

n_●representation findingThe mean fitness estimate of the final gBest of the algorithm ●;

N_avgrepresenting the average fitness evaluation number;

n_avgthe average fitness evaluation number representing the final gBest is found;

N_gBestrepresents the number of gBest;

N_genrepresenting a genetic algebra;

N_runrepresenting the number of independent runs;

N_solrepresenting the number of solutions;

N_varrepresenting the number of variables;

P_gBestrepresents the current gBest (historically best solution);

P_irepresents the ith (i)^th) Current pBest of solutions (the historically best solution of itself);

p_i,jrepresents P_iJ (j) of^th) A variable;

PSO represents a particle swarm optimization algorithm/a particle swarm algorithm;

SSO stands for simplified population optimization algorithm/simplified population algorithm;

t represents an operating time limit;

UM₁representing a univariate update mechanism;

UM_arepresenting an all-variable update mechanism;

X_i,jdenotes the j (j) th^th) Generation i (i)^th) Solving;

x_i,j,krepresents X_gen,solK (k) of^th) A variable;

X_gen,solrepresents the sol solution of the gen generation.

Claims

1. A method of harmonic group optimization, the method comprising the steps of:

step 1, constructing a harmonic step length strategy HSS;

step 2, establishing a univariate updating mechanism UM₁；

Step 3, passing through UM₁Optimizing the SSO by the HSS to obtain the optimized SSO;

and 4, applying the optimized SSO to big data processing.

2. The method of claim 1, wherein in step 1, the method for constructing the harmonic step size strategy HSS comprises: the construction of a harmonic sequence-based HSS is shown as follows:

wherein N is_varIs the number of variables, U_kAnd L_kIs the upper and lower limits of the kth variable, i is the current algebra, k is the index of the current variable; if the sequence of 1,1/2,1/3,1/4 is referred to as a harmonic sequence, the HSS can be expressed based on the harmonic sequence as follows:

3. The method of claim 1, wherein in step 2, a univariate update mechanism UM is established₁The method comprises the following steps: let UM of each solution₁In the method, only one random selection variable is updated, and i is assumed to be the current generation number, x_j,kIs to solve X from the jth_jOf (a) a randomly selected variable of (b),

is obtained by modifying X_jX of_j,kThe resulting time solution yields the following equation:

4. The harmonic cluster optimization method of claim 2 or 3 wherein in step 3 the UM is passed₁And the method for optimizing the SSO by the HSS comprises the following steps:

and step 0, making i-j-gBest-1.

Step 1, by X_jAnd calculating F (X)_j)；

Step 2, if F (X)_gBest)<F(X_j) Let gBest be j;

step 3, if j<N_solLet j equal to j +1 and go to step 1;

step 4, let n^*＝1，N^*50, and order

Wherein k is 1,2, …, N_var；

Step 5, making i ═ i +1 and j ═ 1;

step 6, from X_jIn which a variable, e.g. x, is randomly selected_j,k；

In the step 7, the step of,order to

Step 8, order

step 10, if F (X)_j)<F(X_gBest) Let gBest be j;

step 12, if j<N_solLet j equal j +1 and go to step 6;

step 13, if i<N^*Go to step 5;

step 14. mixing n^*Increase by 1, N^*Increase by 50, and order

Wherein k is 1,2, …, N_varAnd go to step 5.

5. The application of a harmonic group optimization method in big data processing through an artificial neural network as claimed in claim 4, wherein the method is applied as follows:

step A1, collecting big data conforming to the big data type;

step A3, performing dimension reduction on the cleaned data set;

step A8, mixing X in each optimized SSO_jThe variable in the method is decoded into parameters to be optimized of the artificial neural network, the error of the neural network after training a training set and/or a testing set is calculated, and the calculated error is used as the fitness F (X)_j) Inputting the result into the optimized SSO, and obtaining the suitable F (X) from the operation result of the optimized SSO_gBest) Of (2) a final solution X_gBestDecoding parameters of the artificial neural network, and taking the obtained artificial neural network as a classification model;

step A9, classifying the newly collected big data which is in accordance with the big data type through a classification model.

6. The application of a harmonic group optimization method in big data processing by a support vector machine as claimed in claim 4, characterized in that the method is applied as follows:

step B1, collecting big data conforming to the big data type;

step B2, preprocessing and cleaning the acquired big data and extracting features to obtain a feature vector of the big data;

step B3, using the feature vector of the big data as a training data set;

step B5, calculating X_jFitness F (X)_j) Inputting the result into the optimized SSO, and obtaining the suitable F (X) from the operation result of the optimized SSO_gBest) Of (2) a final solution X_gBestDecoding the parameters into parameters of a support vector machine, and taking the obtained support vector machine as a classification model;

and step B6, classifying the newly acquired big data which is in accordance with the big data type through a classification model.